C SC 483Chess and AI: Computation

and CognitionLecture 5

September 24th

Task 2

• Your Goal:by next time– have the bitboard

system up andrunning

– to show:– e.g. click on a piece,

highlight its possiblemoves (graphically)

– or equivalent

Rotated BitboardsLast time we discussed therank and file attacks

• computed using a lookuptable for the rank

• file case reduces to the rankcase if we maintain 90degree rotated bitboards

• Good Reference(from lecture 3, slide 34):

– http://www.cis.uab.edu/hyatt/bitmaps.html

1 11 1 1

rank returns 11101100

10 1 1 1 0 0 0

lsb

msb

byte 8 byte 1

hex

0he

x 1

hex

14he

x 15

Rotated Bitboards• Sliding pieces:

– queen: either diagonal– bishop: either diagonal

• Key idea:– make diagonals consecutive

bits in rotated bitboard• Worked example:

– Leading Diagonal– bitboard is organized as shown

• leading diagonal (╲):

b0b1

b2

b3

b4

b5

b6

b7

2b0

2b1

2b2

2b3

2b4

2b5

2b6

2b7

3b0

2b7 2b6 2b5 2b4 b6 b5 b3 b0b1b2b4b72b02b12b22b3

3b1

3b4

3b5

4b0

4b3

4b4

5b4

6b3

7b1

7b6

8b2

8b5

8b7

Rotated Bitboards• Bitboards

– for the leading diagonalmaintained in parallel with theother bitboards

ldk “leading diagonal white king”ldK “leading diagonal black king”...ldb “leading diagonal white bishop”...ldP “leading diagonal black pawns”

• Computed Bitboardsldwhite = ( ldk | ldq | ldr | ldb | ldk |ldp )ldblack = ( ldK | ldQ | ldr | ldB | ldK |ldP )

• leading diagonal (╲):

b0b1

b2

b3

b4

b5

b6

b7

2b0

2b1

2b2

2b3

2b4

2b5

2b6

2b7

3b4

3b5

4b3

4b4

5b4

6b3

7b1

7b6

8b2

8b5

8b7

Rotated Bitboards• Two arrays/tables needed:

– Find your diagonal by rightshifting the bitmap

– Mask with your diagonal (ofvarying length)

• Example:– ldb = 0x0000000080000000– ldQ = 0x0000000020000000

• look up table:– given a bitmap, find its shift

number– diagonal_shift(ldb) = 28– (ldwhite | ldblack) >> 28 will give

what’s on the diagonal and more

• leading diagonal (╲):

b0b1

b2

b3

b4

b5

b6

b7

2b0

2b1

2b2

2b3

2b4

2b5

2b6

2b7

3b4

3b5

4b3

4b4

5b4

6b3

7b1

7b6

8b2

8b5

8b7

Rotated Bitboards• Two arrays/tables needed:

– Find your diagonal by right shifting thebitmap

– Mask with your diagonal (of varyinglength)

• Example:– ldb = 0x0000000080000000– ldQ = 0x0000000020000000

• look up table:– given a bitmap, find its mask– diagonal_mask(ldb) = FF (8bits long)

• summary:– diagonal(bb) = ((ldwhite | ldblack)

>> diagonal_shift(bb)) &diagonal_mask(bb)

– will give the diagonal

• leading diagonal (╲):

b0b1

b2

b3

b4

b5

b6

b7

2b0

2b1

2b2

2b3

2b4

2b5

2b6

2b7

3b4

3b5

4b3

4b4

5b4

6b3

7b1

7b6

8b2

8b5

8b7

Rotated Bitboards• Access diagonal

– diagonal right shift (>>) mask1 0 0x012 1 0x033 3 0x074 6 0x0F5 10 0x1F6 15 0x3F7 21 0x7F8 28 0xFF9 36 0x7F10 43 0x3F11 49 0x1F12 54 0x0F13 58 0x0714 61 0x0315 63 0x01

• trailing diagonal (╱):

12

3

4

5

7

8

11

12

16

17

22

23

9

10

13

14

18

19

20

21

24

25

26

27

15

28

6

Rotated Bitboards• Computed diagonal can be

looked up using the existingrank attacks tables

– diagonal(bb) = ((ldwhite | ldblack) >> diagonal_shift(bb)) &diagonal_mask(bb)computes a single byte

• Note:– if diagonal is shorter than 8 bits, fill in with 1’s for 8 bit lookup

diagonal(bb) | inv_mask(diagonal_mask(bb))• Examples:

– mask inv_mask– 0xFF 0x00– 0x0F 0xF0

• rank attacks lookup:

1 11 1 1

rank returns 11101100

Rotated Bitboards• define

– ld_moves(ldbb) = rank((( ldwhite |ldblack) >> diagonal_shift(ldbb)) &diagonal_mask(ldbb)) |inv_dmask(diagonal_mask(ldbb)),ldbb >> diagonal_shift(ldbb) &diagonal_mask(ldbb)) <<diagonal_shift(ldbb)

• Worked example: white bishop– ldwhite = ldb = 0x0000000080000000– ldblack = ldQ = 0x0000000020000000– diagonal_shift(ldb) = 28– diagonal_mask(ldbb) = 0xFF– rank((0x00000000A0000000 >> 28) &

0xFF | 0x00, (0x0000000080000000>> 28) & 0xFF) << 28)

– rank(0x0A,0x08) << 28– 0xF6 << 28 = 0x0000000F60000000

• compute diagonal attacks

0 1 0 1 0 0 0 0 (msb)

0 1 1 0 1 1 1 1 (msb)

+ mask out white pieces

Rotated Bitboards• Similar considerations for the

trailing diagonal representation

• Functions (or arrays):diagonal_shift(bb)diagonal_mask(bb)

(described earlier) can be re-used on the understandingthat they apply to the trailingdiagonal representation

• trailing diagonal (╱):

b0

b2

b1

b5

b4

b3

2b1

2b0

b7

b6

2b6

2b5

2b4

2b3

2b2 2b7

3b0

(1,1) (8,1)

(1,8) (8,8)

Rotated Bitboards

• result:

APPROXIMATE CHESS RANKINGS• 1. Complete beginner ( Rating<300)• 2. Beginner (Rating 300-600)• 3. Stronger beginner (Rating 600-900)• 4. Strong beginner (Rating 900-1200)• 5. Intermediate player ( Rating 1200-1400)• 6. Class D player (Rating 1400-1600)• 7.Class C player (Rating 1600-1800)• 8.Class B player ( Rating 1800-1900)• 9. Class A player (Rating 1900-1999)• 10. Expert (Rating 2000-2199)• 11. Master (Rating 2200)• 12. National Master ( Rating 2200 up to about 2300 )• 13. Senior Master (Rating of about 2300 to 2400 )• 13. FIDE Master ( International Rating of 2300 or higher after 24 games)• 14. International Master ( International rating of 2400> and 3 Norms completed )• 15. Grandmaster ( International rating of 2500> and 3 Norms completed )• 16. World Champion ( Best in the world, usually rating of 2750> and the winner of a

match recognized by FIDE )

KARPOV-KASPAROVLINARES 93

BOTVINNIK-CAPABLANCAHolland 1938

One of the most beautiful tactics of that era.Botvinnik was just becoming a top player,while Capablanca was still at his best. Thegame is also famous for being the 1st game

that a Chess Computer “Pioneer” in 1977 wasable to solve not by calculating million moves

but only few and choosing the best out ofthem.

BOTVINNIK-CAPABLANCA

The Opening

The Middlegame fight

The Tactical Calculation

Tactical Execution of the Idea

The Final Struggle by Black

Short Description of the Game• 1. A Normal Chess Opening by both sides.• 2. A power struggle on all 3 sides of the board.• 3. White opens the center and aims at the Black King.• 4. Black destroys white’s Queen side.• 5. White creates a strong Passed Pawn.• 6. White Sacrifices 2 pieces to open the Black King and

attack it.• 7. White threatens a Checkmate or Queen Promotion of

the “E” pawn.• 8. Black seeks Perpetual Chess but cannot find it.• 9. White wins.

HOMEWORKSet-up a chess board ( or use a Computer generated chess board ). Find thisgame (Botvinnik-Capablanca, 1938) in a chess book, use the full notationprovided above or on-line. You can use sources such as Chessbase (Lite),chessgames.com, chesslab.com, chessbase.com or any other to find thegame and possibly some commentaries about the game by Grandmasters.Go move-by-move over the game and find out what the opponents tried to doand what did they possibly miss.

1. What can you tell us about the Nimzo-Indian Opening that was used in thisgame. Its origination, strategic concepts, some examples, names of famouschess players who resorted to this defense when playing black. (15 Pts)

2. Was there a defense for Black anywhere after move 28? Think of your ownsuggestions, or use any sources to help improve Black’s defense. Where doyou think Black went wrong in the game? ( it could be on multiple points ofthe game ) (15 pts)

3. What can you tell me about the “Pioneer” Chess program developed byBotvinnik and what was so special about it? (Extra Credit-5 Pts)

Should be typed,Between 1-2 pages per question.Sources cited.